Cremona's table of elliptic curves

845 = 5 · 13²

Field	Data	Notes
Atkin-Lehner	5- 13+	Signs for the Atkin-Lehner involutions
Class	845a	Isogeny class
Conductor	845	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	313742585 = 5 · 137	Discriminant
Eigenvalues	1 -2 5-  4 -2 13+  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-173,171]	[a1,a2,a3,a4,a6]
j	117649/65	j-invariant
L	1.4929349381889	L(r)(E,1)/r!
Ω	1.4929349381889	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13520bc1 54080p1 7605j1 4225b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 845a1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
1	-2	-	4	-2	+	2	6	-6	2	10	2	6	10	-4	2	-6	2	4	-6	6	-12	16	-2	2

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Quadratic twists for elliptic curve 845a1

-4	8	-3	5	-7	-11	13
13520bc1	54080p1	7605j1	4225b1	41405f1	102245l1	65a1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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